I don't believe there is a fuse for headlights in the fuse box. They depend on fuseable links. At least that's my thinking. The brown wires are the hot ones. You might have a bad bulkhead connector. The only way to isolate the problem is with your volt meter. Do you have a service manual?
The red wire is power to the switch. You should have 12 volt there. Then, with the headlights on, you should have 12 volts at the brown wire. If you don't get 12 volts at the brown wire with the switch on, then you've got a bad switch. You can pull the switch out and test it. With the knob facing away from you, connect one lead of your Ohm meter to the to left terminal, the other lead goes to the brown terminal labelled "9". Pull the switch to on and you should get a closed circuit. If you don't, the switch is bad.